A226706 G.f.: 1 / sqrt(1 + 12*x*G(x)^4 - 16*x*G(x)^5) where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.

1, 2, 22, 256, 3174, 40862, 539376, 7247448, 98684230, 1357638124, 18831752122, 262974273200, 3692853486768, 52102851020154, 738102882420440, 10492839572260176, 149623214762194182, 2139329701502229300, 30661862088900836964, 440404155129948147776

Offset: 0

Author

Paul D. Hanna, Jun 15 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 22*x^2 + 256*x^3 + 3174*x^4 + 40862*x^5 +...
A related series is G(x) = 1 + x*G(x), which begins
G(x) = 1 + x + 6*x^2 + 51*x^3 + 506*x^4 + 5481*x^5 + 62832*x^6 +...
where A(x) = 1/sqrt(1 + 12*x*G(x)^4 - 16*x*G(x)^5).
		

Crossrefs

Cf. A226705, A183160, A002295.

Programs

PARI

{a(n)=local(G=1+x); for(i=0, n,G=1+x*G^6+x*O(x^n)); polcoeff(1/sqrt(1+12*x*G^4-16*x*G^5), n)}
for(n=0, 30, print1(a(n), ", "))

Formula

Sum_{k=0..n} a(n-k)*a(k) = Sum_{k=0..n} C(3*n+2*k,n-k)*C(3*n-2*k,k).

Self-convolution equals A226705.